Even the full-size bottles usually just have a clear stick-on strip with the name of the exact fragrance. Examine your vial more closely and see if there's anything else on there. Some companies, like l'Artisan, don't put the name on the vial, just on the card it's attached to. It could be that if you've lost the card, you've lost the name.
Can you give a fairly detailed description of the scent? One of us might be able to narrow it down to one or two possibilities...